Seismic vibrators have long been used in the seismic data acquisition industry to generate the acoustic signals needed in geophysical exploration. The conventional use of vibrators involves several well-understood steps. First, one or more vibrators are located at a source point on the surface of the earth. Second, the vibrators are activated for several seconds, typically ranging from four to sixteen, with a pilot signal. The pilot signal is typically a sweep signal that varies in frequency during the period of time in which the vibrators are activated. Third, seismic receivers are used to receive and record response data for a period of time equal to the sweep time plus a listen time. The period of time over which data is recorded includes at a minimum the time necessary for the seismic signals to travel to and reflect off of the target reflectors of interest, and for the reflected signals to return to the receivers. Fourth, seismograms are generated by cross correlating the recorded data with either the pilot signal or a reference sweep. Fifth, the sweep and correlation steps are repeated several times, typically four to eight, and the correlations are added together in a process referred to as stacking. Finally, the vibrators are moved to a new source point and the entire process is repeated.
Several problems are known to exist with conventional vibrator technology. First, the correlation process is known to result in correlation side lobes, which can influence the accuracy of the final processed data. Second, vibrator harmonic distortion results in noise, known as harmonic ghosts, after correlation with the pilot. A partial solution to this problem is the use of upsweeping pilot signals, in which the sweep starts at low frequencies and increases to high frequencies. This approach places the correlation ghosts before the main correlation peak where they will not interfere with later, and hence weaker, reflections. In addition, to minimize noise from harmonics, multiple sweeps are performed with incremental phase rotation of the sweeps so that after correlation and stack, the harmonics are reduced. For example, to suppress harmonics through fourth order, four sweeps might be performed with a phase rotation of 360 degrees divided by four, i.e., 0, 90, 180, and 270 degrees. The data are stacked after correlation with harmonics accordingly reduced, although not eliminated. Third, in order to accurately process the recorded data, both the sweep time and a listen time must be included in the recording time of the seismic receivers for each sweep. The listen time is important to ensure that the resulting data from each sweep can be accurately processed. In addition, multiple sweeps are often required to inject sufficient energy into the ground. Multiple short sweeps can result in better data quality than long sweeps through the use of phase rotations to reduce harmonic noise and by reducing ground roll reverberations. However, the use of multiple sweeps with each sweep followed by a listening time limits the rate at which energy can be put into the ground and the survey acquired. Fourth, the recording of high frequencies can be limited by the simultaneous recording of the signals from an array of vibrators, each vibrator at a different position and elevation and having a different coupling with the ground.
The cost of land surveys largely depends on the time it takes to record the survey, and cost is affected by the length of time required to record data at each source station as well as the time it takes to move the vibrators to the next station. The time taken to record data at each source station depends on the number of sweeps, the sweep length, and the listen time. For example, if four 8-second sweeps are performed, each having a 7-second listening time, at least 60 seconds is required at each station. Typical data acquisition systems also require 3-5 seconds before they are ready to start a new record, which can add another 12-20 seconds to the time at the source station. If multiple stations could be recorded simultaneously, or the need for a listening time reduced or eliminated, then less time would be needed for recording the survey, therefore reducing the overall cost of the survey. Similarly, improved methods of reducing side lobe correlations and harmonic ghosts would improve the quality of land surveys.
In 1995, Andersen in U.S. Pat. No. 5,410,517 disclosed a method to cascade vibrator sweeps to eliminate unproductive listening times, while still maintaining the advantages of using multiple short sweeps. The method includes an incremental phase rotation of the sweep segments and the use of a second cascaded sweep with an extra sweep segment to suppress harmonic ghosts after correlation with the reference. For example, but without limitation, in a seismic acquisition program in which it was desired to reduce up to the fourth order harmonic, four sweep segments with an appropriate phase rotation are required. The phase rotation angles could be 0, 90, 180, and 270 degrees, respectively, although other choices could also be made. If eight-second sweep segments were used and 7 seconds listening time is required, then the total record time is 39 seconds. This compares to a standard sweep and listen time for 4 sweeps, which is 60 seconds. Combined with Andersen's prior U.S. Pat. No. 5,347,494, which disclosed a method of producing simple seismic wavelet shapes with minimal side lobe energy, improved quality vibrator data can be obtained. Nevertheless, even with this improved quality data the limitations of the correlation process, problems with harmonics ghosting, and array limitations are present.
Another method used by industry to increase the rate of seismic acquisition is to use more than one vibrator and record multiple source locations simultaneously. Typically, pilot sweeps with different phases or different frequency ranges are used to drive the different vibrators. The data are then correlated with each of the individual pilot sweeps to separate the data. Multiple sweeps are used to increase energy, and the cross correlations are added (stacked). Phase rotation of the sweeps also may be used to reduce harmonics. Separation of the data is imperfect. Instead of clean vibrator records, the separated records may contain residual energy from other vibrators operating simultaneously.
An alternative approach for separating vibrator signals and eliminating harmonics is taken by the High Fidelity Vibratory Seismic Method (HFVS) disclosed in U.S. Pat. Nos. 5,719,821 and 5,721,710 to Sallas, et al. In the HFVS method the recorded seismic data are not correlated with a pilot signal, but instead are inverted using measured vibrator signatures from each sweep and each vibrator. Because the measured signatures include harmonics, the inversion of the corresponding records recovers those harmonics in the processed data, and thereby does not result in additional noise in the data. Because correlation is not used, correlation side lobes do not exist as a potential problem. Furthermore, inversion with a measured vibrator signature can reduce effects from variable vibrator coupling with the earth. However, in this method the vibrator motion for each data record is measured and used in the processing steps. The method includes use of a matrix inversion method to separate the signals from individual vibrators recording simultaneously. The matrix inversion requires that the number of sweeps M be greater than or equal to the number of vibrators N in order to solve a set of linear equations for the N vibrator signals. The ability to separate vibrator responses requires that any two vibrators must differ in at least one of their M sweeps. An advantageous way to accomplish this is to phase-encode the M sweeps, typically with one vibrator at a time sweeping with a phase shift relative to the other vibrators. The M×N vibrator signatures are used to design a filter matrix that converts the M data records into N output records, one per each vibrator. Separation of vibrator records up to 60 dB has been achieved with no visible degradation of the records from simultaneous recordings.
The HFVS method is more fully described in association with FIG. 1, which depicts a typical land-based data acquisition system geometry, and FIG. 2, which depicts typical sweeps for four vibrators which may be used in that data acquisition system. FIG. 1 shows four vibrators 18, 20, 22, and 24, mounted on vehicles 34, 36, 38, and 40. The four different signatures transmitted into the ground during sweep i may be called si1, Si2, Si3, Si4. Each signature is convolved with a different earth reflectivity sequence e1, e2, e3, e4 which includes reflections 26 from the interface 28 between earth layers having different impedances (the product of the density of the medium and the velocity of propagation of acoustic waves in the medium). A trace di recorded at a geophone 30 is a sum of the signature-filtered earth reflectivities for each vibrator. Formulating this mathematically, data trace di(t) recorded for sweep i is:
                                          d            i                    ⁡                      (            t            )                          =                              ∑                          j              =              1                        N                    ⁢                                                    s                ij                            ⁡                              (                t                )                                      ⊗                                          e                j                            ⁡                              (                t                )                                                                        (        1        )            where sij(t)=sweep i from vibrator j, ej(t)=earth reflectivity seen by vibrator j and {circle around (×)} denotes the convolution operator.
Persons skilled in the art will understand the convolution operation and the convolution model upon which Equation (1) is based. Other readers may refer to standard treatises such as the Encyclopedic Dictionary of Exploration Geophysics, by R. E. Sheriff, 4th Ed. (2002), published by the Society of Exploration Geophysicists. (See the definitions of “convolution” and “convolutional model.”) The noise term in Sheriff's definition of “convolutional model” has been neglected in Equation (1). This model is a consequence of the concept that each reflected seismic wave causes its own effect at each geophone, independent of what other waves are affecting the geophone, and that the geophone response is simply the sum (linear superposition) of the effects of all the waves.
Thus, in this method N vibrators radiate M≧N sweeps into the earth, resulting in M recorded data traces. The HFVS method involves finding an operator, by solving a set of linear equations based on the known M×N vibrator signatures, that finds the set of N earth reflectivities that best predicts the recorded data. In the frequency domain, i.e., after Fourier transformation, the set of equations represented by Equation (1) are linear and can be written:
                                          D            i                    ⁡                      (            f            )                          =                              ∑                          j              =              1                        N                    ⁢                                                    s                ij                            ⁡                              (                f                )                                      ⁢                                          E                j                            ⁡                              (                f                )                                                                        (        2        )            or, in matrix form for M sweeps and N vibrators,
                                          [                                                                                S                    11                                                                                        S                    12                                                                    ·                                                                      S                                          1                      ⁢                                                                                          ⁢                      N                                                                                                                                        S                    21                                                                                        S                    22                                                                    ·                                                                      S                                          2                      ⁢                                                                                          ⁢                      N                                                                                                                                        S                    31                                                                                        S                    32                                                                    ·                                                                      S                                          3                      ⁢                                                                                          ⁢                      N                                                                                                                                        S                    41                                                                                        S                    42                                                                    ·                                                                      S                                          4                      ⁢                                                                                          ⁢                      N                                                                                                                    ·                                                  ·                                                  ·                                                  ·                                                                                                  S                                          M                      ⁢                                                                                          ⁢                      1                                                                                                            S                                          M                      ⁢                                                                                          ⁢                      2                                                                                        ·                                                                      S                    MN                                                                        ]                    ⁡                      [                                                                                E                    1                                                                                                                    E                    2                                                                                                ·                                                                                                  E                    N                                                                        ]                          =                  [                                                                      D                  1                                                                                                      D                  2                                                                                                      D                  3                                                                                                      D                  4                                                                                    ·                                                                                      D                  M                                                              ]                                    (        3        )                                or                                                                          S          ⁢                      E            →                          =                  D          →                                    (        4        )            If the number of sweeps is equal to the number of vibrators, this system of simultaneous equations can be solved for {right arrow over (E)}:{right arrow over (E)}=F{right arrow over (D)}  (5)whereF=(S)−1.  (6)F is the filter or operator which when applied to the data separates it into individual vibrator records.
For M≧N, Equation (4) may be solved by the method of least squares. For this more general situation, Equation (4) can be writtenS*S{right arrow over (E)}=S*{right arrow over (D)}  (7)where S* is the conjugate transpose of matrix S. Then,{right arrow over (E)}=(S*S)−1S*{right arrow over (D)},  (8)and the filter F becomesF=(S*S)−1S*.  (9)
The HFVS method can be used to record multiple source points simultaneously using a number of vibrators, but the use of more vibrators requires more individual sweeps each with its own listening time. It was previously not thought possible to eliminate the listening time, because the M sweep records must be separate unrelated measurements in order to solve the set of linear equations, i.e., otherwise the M equations (involving N unknowns) would not be independent. If the sweeps are cascaded without a listening time, then the reflection data from one segment would interfere with data from the subsequent sweep segment. In addition, there would not be a one-to-one correspondence between the data and the measured vibrator motions which represent the signatures put into the ground, so that harmonics would not be handled properly. The present invention solves these problems.